Critical slowing down exponents in quenched disordered spin models for structural glasses: Random Orthogonal and related models

TL;DR

This paper uses a new static method to exactly compute critical slowing down exponents in mean-field spin-glass models, including the SK, p-spin, and Random Orthogonal models, linking them to Mode-Coupling-Theory predictions.

Contribution

It introduces a novel static approach to precisely calculate critical exponents in mean-field spin-glass models, clarifying their relation to MCT.

Findings

Exact computation of critical exponents in various spin-glass models.

Validation of MCT predictions for these models.

Unified framework linking static properties to dynamic exponents.

Abstract

An important prediction of Mode-Coupling-Theory (MCT) is the relationship between the power- law decay exponents in the {\beta} regime. In the original structural glass context this relationship follows from the MCT equations that are obtained making rather uncontrolled approximations and {\lambda} has to be treated like a tunable parameter. It is known that a certain class of mean-field spin-glass models is exactly described by MCT equations. In this context, the physical meaning of the so called parameter exponent {\lambda} has recently been unveiled, giving a method to compute it exactly in a static framework. In this paper we exploit this new technique to compute the critical slowing down exponents in a class of mean-field Ising spin-glass models including, as special cases, the Sherrington-Kirkpatrick model, the p-spin model and the Random Orthogonal model.